kol isha, agency, and women reading torah
There is an issue in halacha called kol isha, which literally means "a woman's voice". The idea is that a woman's voice -- specifically a singing voice, according to B'rachot 24a -- will arouse men in the same way that seeing her hair (or certain body parts, and I don't just mean the naughty bits) will. So just as women are to cover their hair and wear modest garments to keep men from sinning, so too are they to refrain from singing around men. (Well, at least solo; being in a group can mitigate.)
I'd long assumed that kol isha is the reason women can't read torah (except in women's groups) in traditional communities. But I've thought of an argument against that position, which probably means that either the argument is wrong or this isn't a kol-isha issue to begin with. (I tend to assume that no halachic argument that turns out to be correct would be original to me, because I don't have the vast knowledge base yet.)
Ok, here goes. There is a state that people and objects can be in called tamei, which is a sort of ritual impurity. (This is sometimes translated as "unclean", but it has nothing to do with physical cleanliness.) If, for example, you come into contact with a corpse, you are tamei for a period of time. You can transmit that status to objects that you touch, and they too are tamei for a period of time. The only time this really matters is in worship -- it really only mattered when the temple stood (nothing tamei inside the courtyard), but I wouldn't be surprised if the concept applies to worship more generally in some ways. (Like, can a coroner ever lead services? I have no idea. But this is a tangent.)
I have learned (can't cite a source but believe it to be valid) that a sefer torah (a torah scroll) can never become tamei, no matter what it comes into contact with. (It can become non-kosher (pasul), but that's completely different.) So, why can't a sefer torah be tamei? Because it contains words of torah, which are inherently holy and can't be made impure. If so for the written form of torah, so too for the oral form? Isn't chanting torah, conveying the words from the sefer torah, inherently holy (and thus not lewd or suggestive)? Can such a reading (if done correctly) be made inappropriate in any way?
There are arguments (having to do with agency) for why women can't lead services, but torah-reading is different. Men are obligated to pray and can't be led by a woman who isn't obligated, but no one is obligated to read torah. People are obligated to hear torah being read. So I don't think the agency argument applies.
I can think of two issues that would arise from this. First, if the prohibition really is about kol isha, wouldn't that imply that a woman could read torah but not chant it? Kol isha is about singing. (And I've been to traditional congregations where the reader read without chanting, so this seems to be permitted.) And second, if agency is really about doing versus hearing as I've speculated, does that mean that women can do other things which we must hear but not necessarily do, like blowing the shofar on Rosh Hashana and reading the megillah on Purim?
I plan to ask my rabbi about this when we meet next week, since it was studying kol isha with him that set this speculation in motion to begin with.

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A firmly entrenched custom in some communities, however.